14-11-2012, 02:44 PM
Air-Gap Convection in Rotating Electrical Machines
[attachment=39441]
Abstract
This paper reviews the convective heat transfer
within the air gap of both cylindrical and disk geometry rotating
electrical machines, including worked examples relevant to
fractional horsepower electrical machines. Thermal analysis of
electrical machines is important because torque density is limited
by maximum temperature. Knowledge of surface convective heat
transfer coefficients is necessary for accurate thermal modeling,
for example, using lumped parameter models. There exists a wide
body of relevant literature, but much of it has traditionally been in
other application areas, dominated by mechanical engineers, such
as gas turbine design. Particular attention is therefore given to the
explanation of the relevant nondimensional parameters and to the
presentation of measured convective heat transfer correlations for
a wide variety of situations from laminar to turbulent flow at small
and large gap sizes for both radial-flux and axial-flux electrical
machines.
INTRODUCTION
THE electromagnetic analysis of motors and generators is a
mature subject; in contrast, the thermal and aerodynamic
aspects of electrical machine design have been less thoroughly
researched to date [1]. Modern machines must be compact,
light, and torque dense and are often required to withstand
extreme environmental and loading conditions. Knowledge of
the airflow in a machine is crucial for design purposes, particularly
where air-gap convection limits heat transfer. The
surface convective heat transfer coefficients, important for the
calculation of temperatures, are complex functions of geometry
and fluid mechanics. This paper seeks to give an overview of the
state of the art in airflow and convection within the air gap in
cylindrical- and disk-type machines, with a particular emphasis
on experimentally measured convection data in the form of
correlations that can be applied during the design. It also seeks
to summarize the typical flow patterns that might arise, some of
which are quite counterintuitive. Other related thermal topics,
such as lumped parameter (LP) modeling, radiation heat transfer,
thermal contact resistances, and finite-element analysis, are
not discussed in detail since they have been covered elsewhere,
e.g., in [2] and [3].
PREVIOUS REVIEWS
There are relatively few review papers on the subject
of airflow and convection in rotating electrical machines.
Boglietti et al. [2] reviewed the thermal analysis of electrical
machines with a particular focus on LP models. Staton et al. [3]
also reviewed the more challenging areas in thermal analysis,
which include contact resistances, stator winding conductivity,
and convection coefficients, particularly around end windings
where there are complex flow paths. Staton and Cavagnino
[10] reviewed convection in electrical machines, focusing on
correlations for natural convection around the external casings
of cylindrical geometry machines and also on correlatons for
forced cooling with fans or water jackets. They included a small
section on air-gap heat transfer. Disk-type machine geometries
were not considered.
CYLINDRICAL GEOMETRY MACHINES
Cylindrical (or “drum”) geometry electrical machines are
the most common type of electrical machine. The air gap is
an annulus formed between two concentric cylinders. The airgap
magnetic field lines are oriented in the radial direction,
so these are also called radial-flux machines. There are many
different machine types, e.g., induction machines, PMbrushless
machines, and switched reluctance machines. Flow and heat
transfer in this geometry is also important to a wide number of
other applications from shafts and axles to spinning projectiles
to gas turbine engines.
Airflow in the Rotor–Stator Gap
Couette flow is the term used to describe the flow between
two surfaces that are in close proximity such that the flow
is dominated by viscous effects and inertial effects which are
negligible. In cylindrical coordinates, this involves the flow in
an annulus, and the Navier–Stokes equations can be solved
exactly by analytical techniques, subject to a number of significant
assumptions. The Couette flow in an annulus with
rotation characterizes a system in which dynamic equilibrium
exists between the radial forces and the radial pressure gradient.
However, when it is not possible for the radial pressure gradient
and the viscous forces to dampen out and restore the changes
in the centrifugal forces caused by small disturbances in the
flow, the fluid motion is unstable and results in a secondary
flow. A simple criterion for determining the onset of instability
was developed by Rayleigh [12]. In essence, the criterion
determines whether the force due to inward radial pressure
is adequate to maintain inward centripetal acceleration for an
arbitrary element of fluid.
Airflow in the Rotor–Stator Gap
A large body of analytical, numerical, and experimental research
has been undertaken concerning airflow and heat transfer
of a disk system. This is relevant to electrical machines, gas
turbines, turbochargers, brake disks, and many other types of
machine. Dorfman’s book [24] concentrates on analytical solutions,
with some experimental results. The book by Owen and
Rogers [25] gives a comprehensive review of various analytical
solutions and compares these with experimental data for free
disk and rotor–stator systems with and without superposed flow,
including heat transfer.
The simplest kind of rotating disk system is the “free disk,”
an infinite-radius rotating disk in a fluid. This was originally
examined by von Kármán [26] who found a solution to the
Navier–Stokes equations showing that the disk drags fluid from
the rotor center to the outside edge, at the same time drawing
fresh fluid inward axially as shown in Fig. 3. By assuming
axisymmetry, he reduced the partial differential equations to a
set of four coupled ordinary differential equations and solved
the nondimensionalized equations for radial, tangential, and
axial velocity components and pressure as a function of axial
distance, by using approximate analytical (momentum-integral)
methods, for both laminar flow and turbulent flow.
CONCLUSION
The prediction of temperatures in electrical machines is vital
to ensure that the designs deliver the required performance at
the lowest cost. This paper has focused on air-gap convective
heat transfer and has sought to give an overview of the work
in this area, collecting and summarizing the key correlations
and findings, including worked examples which are particularly
relevant to smaller machines. Many correlations have arisen
from work on turbomachinery but are equally applicable in
electrical machine design and have not been presented previously
in this context. It is hoped that designers can directly
apply these correlations within thermal models to predict
temperatures.
[attachment=39441]
Abstract
This paper reviews the convective heat transfer
within the air gap of both cylindrical and disk geometry rotating
electrical machines, including worked examples relevant to
fractional horsepower electrical machines. Thermal analysis of
electrical machines is important because torque density is limited
by maximum temperature. Knowledge of surface convective heat
transfer coefficients is necessary for accurate thermal modeling,
for example, using lumped parameter models. There exists a wide
body of relevant literature, but much of it has traditionally been in
other application areas, dominated by mechanical engineers, such
as gas turbine design. Particular attention is therefore given to the
explanation of the relevant nondimensional parameters and to the
presentation of measured convective heat transfer correlations for
a wide variety of situations from laminar to turbulent flow at small
and large gap sizes for both radial-flux and axial-flux electrical
machines.
INTRODUCTION
THE electromagnetic analysis of motors and generators is a
mature subject; in contrast, the thermal and aerodynamic
aspects of electrical machine design have been less thoroughly
researched to date [1]. Modern machines must be compact,
light, and torque dense and are often required to withstand
extreme environmental and loading conditions. Knowledge of
the airflow in a machine is crucial for design purposes, particularly
where air-gap convection limits heat transfer. The
surface convective heat transfer coefficients, important for the
calculation of temperatures, are complex functions of geometry
and fluid mechanics. This paper seeks to give an overview of the
state of the art in airflow and convection within the air gap in
cylindrical- and disk-type machines, with a particular emphasis
on experimentally measured convection data in the form of
correlations that can be applied during the design. It also seeks
to summarize the typical flow patterns that might arise, some of
which are quite counterintuitive. Other related thermal topics,
such as lumped parameter (LP) modeling, radiation heat transfer,
thermal contact resistances, and finite-element analysis, are
not discussed in detail since they have been covered elsewhere,
e.g., in [2] and [3].
PREVIOUS REVIEWS
There are relatively few review papers on the subject
of airflow and convection in rotating electrical machines.
Boglietti et al. [2] reviewed the thermal analysis of electrical
machines with a particular focus on LP models. Staton et al. [3]
also reviewed the more challenging areas in thermal analysis,
which include contact resistances, stator winding conductivity,
and convection coefficients, particularly around end windings
where there are complex flow paths. Staton and Cavagnino
[10] reviewed convection in electrical machines, focusing on
correlations for natural convection around the external casings
of cylindrical geometry machines and also on correlatons for
forced cooling with fans or water jackets. They included a small
section on air-gap heat transfer. Disk-type machine geometries
were not considered.
CYLINDRICAL GEOMETRY MACHINES
Cylindrical (or “drum”) geometry electrical machines are
the most common type of electrical machine. The air gap is
an annulus formed between two concentric cylinders. The airgap
magnetic field lines are oriented in the radial direction,
so these are also called radial-flux machines. There are many
different machine types, e.g., induction machines, PMbrushless
machines, and switched reluctance machines. Flow and heat
transfer in this geometry is also important to a wide number of
other applications from shafts and axles to spinning projectiles
to gas turbine engines.
Airflow in the Rotor–Stator Gap
Couette flow is the term used to describe the flow between
two surfaces that are in close proximity such that the flow
is dominated by viscous effects and inertial effects which are
negligible. In cylindrical coordinates, this involves the flow in
an annulus, and the Navier–Stokes equations can be solved
exactly by analytical techniques, subject to a number of significant
assumptions. The Couette flow in an annulus with
rotation characterizes a system in which dynamic equilibrium
exists between the radial forces and the radial pressure gradient.
However, when it is not possible for the radial pressure gradient
and the viscous forces to dampen out and restore the changes
in the centrifugal forces caused by small disturbances in the
flow, the fluid motion is unstable and results in a secondary
flow. A simple criterion for determining the onset of instability
was developed by Rayleigh [12]. In essence, the criterion
determines whether the force due to inward radial pressure
is adequate to maintain inward centripetal acceleration for an
arbitrary element of fluid.
Airflow in the Rotor–Stator Gap
A large body of analytical, numerical, and experimental research
has been undertaken concerning airflow and heat transfer
of a disk system. This is relevant to electrical machines, gas
turbines, turbochargers, brake disks, and many other types of
machine. Dorfman’s book [24] concentrates on analytical solutions,
with some experimental results. The book by Owen and
Rogers [25] gives a comprehensive review of various analytical
solutions and compares these with experimental data for free
disk and rotor–stator systems with and without superposed flow,
including heat transfer.
The simplest kind of rotating disk system is the “free disk,”
an infinite-radius rotating disk in a fluid. This was originally
examined by von Kármán [26] who found a solution to the
Navier–Stokes equations showing that the disk drags fluid from
the rotor center to the outside edge, at the same time drawing
fresh fluid inward axially as shown in Fig. 3. By assuming
axisymmetry, he reduced the partial differential equations to a
set of four coupled ordinary differential equations and solved
the nondimensionalized equations for radial, tangential, and
axial velocity components and pressure as a function of axial
distance, by using approximate analytical (momentum-integral)
methods, for both laminar flow and turbulent flow.
CONCLUSION
The prediction of temperatures in electrical machines is vital
to ensure that the designs deliver the required performance at
the lowest cost. This paper has focused on air-gap convective
heat transfer and has sought to give an overview of the work
in this area, collecting and summarizing the key correlations
and findings, including worked examples which are particularly
relevant to smaller machines. Many correlations have arisen
from work on turbomachinery but are equally applicable in
electrical machine design and have not been presented previously
in this context. It is hoped that designers can directly
apply these correlations within thermal models to predict
temperatures.